TASE-Stabilized Time-Evolving Natural Gradient Methods for Diffusion-Dominated PDEs

This paper presents the TASE-stabilized Time-Evolving Natural Gradient (TENG) method for evolving neural approximations of time-dependent partial differential equations. The approach projects time-discrete target states onto the neural-network manifold through local natural-gradient iterations. For stiff diffusion-dominated problems, where explicit Runge-Kutta methods suffer from severe stability restrictions, TASE provides stabilization by preventing stage targets from exceeding the locally reachable region caused by high-frequency diffusive components.